/*=========================================================================
 *
 *  Copyright UMC Utrecht and contributors
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *        http://www.apache.org/licenses/LICENSE-2.0.txt
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
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 *=========================================================================*/
/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkAdvancedSimilarity3DTransform.txx,v $
  Language:  C++
  Date:      $Date: 2007-11-27 16:04:48 $
  Version:   $Revision: 1.9 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef _itkAdvancedSimilarity3DTransform_hxx
#define _itkAdvancedSimilarity3DTransform_hxx

#include "itkAdvancedSimilarity3DTransform.h"
#include "vnl/vnl_math.h"
#include "vnl/vnl_det.h"

namespace itk
{

// Constructor with default arguments
template< class TScalarType >
AdvancedSimilarity3DTransform< TScalarType >
::AdvancedSimilarity3DTransform() :
  Superclass( OutputSpaceDimension, ParametersDimension )
{
  m_Scale = 1.0;
  this->PrecomputeJacobianOfSpatialJacobian();
}


// Constructor with arguments
template< class TScalarType >
AdvancedSimilarity3DTransform< TScalarType >::AdvancedSimilarity3DTransform( unsigned int outputSpaceDim,
  unsigned int paramDim ) :
  Superclass( outputSpaceDim, paramDim )
{}

// Constructor with arguments
template< class TScalarType >
AdvancedSimilarity3DTransform< TScalarType >::AdvancedSimilarity3DTransform( const MatrixType & matrix,
  const OutputVectorType & offset ) :
  Superclass( matrix, offset )
{}

// Set the scale factor
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::SetScale( ScaleType scale )
{
  m_Scale = scale;
  this->ComputeMatrix();
}


// Directly set the matrix
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::SetMatrix( const MatrixType & matrix )
{
  //
  // Since the matrix should be an orthogonal matrix
  // multiplied by the scale factor, then its determinant
  // must be equal to the cube of the scale factor.
  //
  double det = vnl_det( matrix.GetVnlMatrix() );

  if( det == 0.0 )
  {
    itkExceptionMacro( << "Attempting to set a matrix with a zero determinant" );
  }

  //
  // A negative scale is not acceptable
  // It will imply a reflection of the coordinate system.
  //

  double s = std::cbrt( det );

  //
  // A negative scale is not acceptable
  // It will imply a reflection of the coordinate system.
  //
  if( s <= 0.0 )
  {
    itkExceptionMacro( << "Attempting to set a matrix with a negative trace" );
  }

  MatrixType testForOrthogonal = matrix;
  testForOrthogonal /= s;

  const double tolerance = 1e-10;
  if( !this->MatrixIsOrthogonal( testForOrthogonal, tolerance ) )
  {
    itkExceptionMacro( << "Attempting to set a non-orthogonal matrix (after removing scaling)" );
  }

  typedef AdvancedMatrixOffsetTransformBase< TScalarType, 3 > Baseclass;
  this->Baseclass::SetMatrix( matrix );
  this->PrecomputeJacobianOfSpatialJacobian();
}


// Set Parameters
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::SetParameters( const ParametersType & parameters )
{

  itkDebugMacro( << "Setting parameters " << parameters );

  // Transfer the versor part

  AxisType axis;

  double norm = parameters[ 0 ] * parameters[ 0 ];
  axis[ 0 ] = parameters[ 0 ];
  norm     += parameters[ 1 ] * parameters[ 1 ];
  axis[ 1 ] = parameters[ 1 ];
  norm     += parameters[ 2 ] * parameters[ 2 ];
  axis[ 2 ] = parameters[ 2 ];
  if( norm > 0 )
  {
    norm = std::sqrt( norm );
  }

  double epsilon = 1e-10;
  if( norm >= 1.0 - epsilon )
  {
    axis = axis / ( norm + epsilon * norm );
  }
  VersorType newVersor;
  newVersor.Set( axis );
  this->SetVarVersor( newVersor );
  m_Scale = parameters[ 6 ]; // must be set before calling ComputeMatrix();
  this->ComputeMatrix();

  itkDebugMacro( << "Versor is now " << this->GetVersor() );

  // Transfer the translation part
  TranslationType newTranslation;
  newTranslation[ 0 ] = parameters[ 3 ];
  newTranslation[ 1 ] = parameters[ 4 ];
  newTranslation[ 2 ] = parameters[ 5 ];
  this->SetVarTranslation( newTranslation );
  this->ComputeOffset();

  // Modified is always called since we just have a pointer to the
  // parameters and cannot know if the parameters have changed.
  this->Modified();

  itkDebugMacro( << "After setting parameters " );
}


//
// Get Parameters
//
// Parameters are ordered as:
//
// p[0:2] = right part of the versor (axis times std::sin(t/2))
// p[3:5} = translation components
// p[6:6} = scaling factor (isotropic)
//

template< class TScalarType >
const typename AdvancedSimilarity3DTransform< TScalarType >::ParametersType
& AdvancedSimilarity3DTransform< TScalarType >
::GetParameters( void ) const
{
  itkDebugMacro( << "Getting parameters " );

  this->m_Parameters[ 0 ] = this->GetVersor().GetX();
  this->m_Parameters[ 1 ] = this->GetVersor().GetY();
  this->m_Parameters[ 2 ] = this->GetVersor().GetZ();

  // Transfer the translation
  this->m_Parameters[ 3 ] = this->GetTranslation()[ 0 ];
  this->m_Parameters[ 4 ] = this->GetTranslation()[ 1 ];
  this->m_Parameters[ 5 ] = this->GetTranslation()[ 2 ];

  this->m_Parameters[ 6 ] = this->GetScale();

  itkDebugMacro( << "After getting parameters " << this->m_Parameters );

  return this->m_Parameters;
}

// Set parameters
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >::GetJacobian( const InputPointType & p,
  JacobianType & j,
  NonZeroJacobianIndicesType & nzji ) const
{
  // Initialize the Jacobian. Resizing is only performed when needed.
  // Filling with zeros is needed because the lower loops only visit
  // the nonzero positions.
  j.SetSize( OutputSpaceDimension, ParametersDimension );
  j.Fill( 0.0 );

  // Some helper variables
  const InputVectorType                 pp  = p - this->GetCenter();
  const JacobianOfSpatialJacobianType & jsj = this->m_JacobianOfSpatialJacobian;

  /** Compute dR/dmu * (p-c) */
  for( unsigned int dim = 0; dim < SpaceDimension; ++dim )
  {
    const InputVectorType column = jsj[ dim ] * pp;
    for( unsigned int i = 0; i < SpaceDimension; ++i )
    {
      j( i, dim ) = column[ i ];
    }
  }

  // compute Jacobian with respect to the translation parameters
  j[ 0 ][ 3 ] = 1.0;
  j[ 1 ][ 4 ] = 1.0;
  j[ 2 ][ 5 ] = 1.0;

  // compute Jacobian with respect to the scale parameter
  const MatrixType &    matrix = this->GetMatrix();
  const InputVectorType mpp    = matrix * pp;
  j[ 0 ][ 6 ] = mpp[ 0 ] / m_Scale;
  j[ 1 ][ 6 ] = mpp[ 1 ] / m_Scale;
  j[ 2 ][ 6 ] = mpp[ 2 ] / m_Scale;

  // Copy the constant nonZeroJacobianIndices
  nzji = this->m_NonZeroJacobianIndices;
}


// Set the scale factor
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::ComputeMatrix()
{
  this->Superclass::ComputeMatrix();
  MatrixType newMatrix = this->GetMatrix();
  newMatrix *= m_Scale;
  this->SetVarMatrix( newMatrix );
  this->PrecomputeJacobianOfSpatialJacobian();
}


/** Compute the matrix */
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::ComputeMatrixParameters( void )
{
  MatrixType matrix = this->GetMatrix();

  m_Scale = std::cbrt( vnl_det( matrix.GetVnlMatrix() ) );

  matrix /= m_Scale;

  VersorType v;
  v.Set( matrix );
  this->SetVarVersor( v );
  this->PrecomputeJacobianOfSpatialJacobian();

}


// Precompute Jacobian of Spatial Jacobian
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >
::PrecomputeJacobianOfSpatialJacobian( void )
{
  if( ParametersDimension < 7 )
  {
    return;
  }

  /** The Jacobian of spatial Jacobian remains constant, so is precomputed */
  JacobianOfSpatialJacobianType & jsj = this->m_JacobianOfSpatialJacobian;
  jsj.resize( ParametersDimension );

  typedef typename VersorType::ValueType ValueType;

  // compute derivatives with respect to rotation
  const ValueType vx = this->GetVersor().GetX();
  const ValueType vy = this->GetVersor().GetY();
  const ValueType vz = this->GetVersor().GetZ();
  const ValueType vw = this->GetVersor().GetW();

  const double vxx = vx * vx;
  const double vyy = vy * vy;
  const double vzz = vz * vz;
  const double vww = vw * vw;

  const double vxy = vx * vy;
  const double vxz = vx * vz;
  const double vxw = vx * vw;

  const double vyz = vy * vz;
  const double vyw = vy * vw;

  const double vzw = vz * vw;

  jsj[ 0 ]( 0, 0 ) = 0.0;     jsj[ 0 ]( 0, 1 ) = vyw + vxz; jsj[ 0 ]( 0, 2 ) = vzw - vxy;
  jsj[ 0 ]( 1, 0 ) = vyw - vxz; jsj[ 0 ]( 1, 1 ) = -2.0 * vxw; jsj[ 0 ]( 1, 2 ) = vxx - vww;
  jsj[ 0 ]( 2, 0 ) = vzw + vxy; jsj[ 0 ]( 2, 1 ) = vww - vxx; jsj[ 0 ]( 2, 2 ) = -2.0 * vxw;
  jsj[ 0 ]        *= ( this->m_Scale * 2.0 / vw );

  jsj[ 1 ]( 0, 0 ) = -2.0 * vyw; jsj[ 1 ]( 0, 1 ) = vxw + vyz; jsj[ 1 ]( 0, 2 ) = vww - vyy;
  jsj[ 1 ]( 1, 0 ) = vxw - vyz; jsj[ 1 ]( 1, 1 ) = 0.0;     jsj[ 1 ]( 1, 2 ) = vzw + vxy;
  jsj[ 1 ]( 2, 0 ) = vyy - vww; jsj[ 1 ]( 2, 1 ) = vzw - vxy; jsj[ 1 ]( 2, 2 ) = -2.0 * vyw;
  jsj[ 1 ]        *= ( this->m_Scale * 2.0 / vw );

  jsj[ 2 ]( 0, 0 ) = -2.0 * vzw; jsj[ 2 ]( 0, 1 ) = vzz - vw;  jsj[ 2 ]( 0, 2 ) = vxw - vyz;
  jsj[ 2 ]( 1, 0 ) = vww - vzz; jsj[ 2 ]( 1, 1 ) = -2.0 * vzw; jsj[ 2 ]( 1, 2 ) = vyw + vxz;
  jsj[ 2 ]( 2, 0 ) = vxw + vyz; jsj[ 2 ]( 2, 1 ) = vyw - vxz; jsj[ 2 ]( 2, 2 ) = 0.0;
  jsj[ 2 ]        *= ( this->m_Scale * 2.0 / vw );

  for( unsigned int par = 3; par < 7; ++par )
  {
    jsj[ par ].Fill( 0.0 );
  }
  if( std::abs( this->m_Scale ) > 0 )
  {
    jsj[ 6 ] = this->GetMatrix().GetVnlMatrix() / this->m_Scale;
  }
}


// Print self
template< class TScalarType >
void
AdvancedSimilarity3DTransform< TScalarType >::PrintSelf( std::ostream & os, Indent indent ) const
{
  Superclass::PrintSelf( os, indent );
  os << indent << "Scale = " << m_Scale << std::endl;
}


} // namespace

#endif
